With regard to an engine brake running mode performed with engine brake applied by driven rotation of an engine while the engine is coupled to wheels, an inertia running mode performed with an engine brake force made lower than that of the engine brake running mode is conceived for extending a running distance and improving fuel consumption. A device described in Patent Document 1 is an example thereof and, two types of control modes are proposed as (a) a first inertia running mode performed with rotation of the engine stopped and (b) a second inertia running mode performed with the engine kept rotating. Specifically, the first inertia running mode is a free-run inertia running mode in which a clutch is released to separate the engine from the wheels while fuel supply to the engine is stopped to stop rotation, and the second inertia running mode is a neutral inertia running mode performed by supplying fuel to allow the engine to operate (perform self-sustaining rotation) while a clutch is released to separate the engine from the wheels. The inertia running mode is performed in either mode without particular distinction under certain conditions.